Answer:
Side c = 22.1
Angle A = 36.7°
Angle B = 53.2°
Angle C = 90.1°
Explanation:
Triangle ABC is a right angle
Where given sides
a = 13.2
b = 17.7
We can find c using Pythagoras Theorem
Pythagoras Theorem for a right angle triangle=
c² = a² + b²
c = √(a² + b²)
c = √(13.2² + 17.7²)
c = 22.08008
≈To the nearest tenth = 22.1
We can solve for Angles A, B, C using Cosine rule
Angle A
a² = b² + c² - 2bc × Cos A
Cos A = b² + c² - a²/2bc
A = Arc cos ( b² + c² - a²/2bc)
A = Arc cos ( 17.7² + 22.1² - 13.2²/2 × 17.7 × 22.1)
A = 36.67563°
≈ To the nearest tenth = 36.7°
Angle B
b² = a² + c² - 2ac × Cos B
Cos B = a² + c² - b²/2ac
B = Arc cos (a² + c² - b²/2ac)
B = Arc cos(13.2² + 22.1² - 17.7²/ 2 × 13.2 ×22.1)
B = 53.21647°
≈Approximately to the nearest tenth = 53.2°
Angle C
c² = a² + b² - 2ab × Cos C
Cos C = a² + b² - c²/2ab
C = Arc cos ( a² + b² - c²/2ab)
C = Arc cos ( 13.2² + 17.7² - 22.1²/2 × 13.2 × 17.7)
C = 90.1079°
≈ to the nearest tenth = 90.1°